1. Solar neutrinos and oscillations
Diego Cauz
18 luglio 2018

2. A journey to the Sun
F. W. Aston discovered that a He atom has a mass defect to four H atoms of 1 part in 120
A. Eddington proposed (1920) that the Sun produces heat and light by means of a nuclear transformation of H into He

3. The CNO cycle
H. Bethe proposed a cycle of nuclear transformation for carbon-containing stars (CNO cycle)
globally
energy

4. Sun-like stars
The CNO cycle, works only if the star contains carbon and its T > 20 millions K
In the Sun carbon is rare and T ~ 15 millions K  a different process is necessary
Bethe found a solution (1939):
for Sun-like stars, H atoms are decomposed into protons and electrons
when two protons collide, the nuclear fusion of the two is possible

5. The pp chain energy Globally
Positrons annihilate with electrons producing gamma rays
All gamma rays bounce repeatedly with charged particles, losing energy in their way towards the surface
At last they emerge from the star as visible light after thousands of centuries
energy

6. Solar neutrinos
The neutrinos, instead, would traverse the Sun unimpeded and reach the Earth in about eigth minutes
Bethe’s theory explained the facts and predicted the production of neutrinos
But in 1939 the neutrino was still considered just a theoretical construction
This changed after Pontecorvo’s 1946 paper and Cowan and Reines’ 1956 antineutrino discovery
The possibility to verify Bethe’s theory, searching for solar neutrinos was considered

7. Another ‘failure’ of Davis’
If solar neutrinos were produced in the CNO cycle, Davis’ apparatus could detect them
But Davis’ try failed so
either the idea of solar neutrinos was wrong
or the CNO cycle was not important to the Sun
Actually in the Sun the dominant process is the pp chain whose neutrinos have insufficient energy (less than one half) for the Cl reaction (860 keV) in Davis’ experiment

8. Good news... In the pp chain one He4 nucleus is produced
He4 has kept accumulating in the Sun for 5 billions years
it is possible that
In 1959 two nuclear physicists* found that berillium-7 production was 1,000 times more probable than expected
7Be, on its turn, can fuse with a proton, producing boron-8
8B decays generating a neutrino with an energy of 14 MeV
and this energy is well over the Cl threshold of Davis’ experiment
* H. D. Holmgren and R. L. Johnston

9. ... and bad news
This encouraged Davis and Calvin to start a new experiment (1959), with the Savannah River detector
To reduce the cosmic-ray background, the experiment moved in a mine 700 meters underground
Unfortunately nuclear physics experiments found that the probability for Be7-p fusion was very small
and Davis again could not find any convincing evidence of solar neutrinos

10. Bahcall & Davis
J. Bahcall: the probability of weak interactions in the stars must be higher than in the lab on Earth
He computed the probability of the Be7-p fusion: the result (1963) was not encouraging
The probability in the Sun was higher than on Earth, but a 4000-liter detector would capture one neutrino in 100 days
Davis thought of a detector 100 times bigger
To suppress the cosmic-ray backgound, they decided the experiment had to be moved 1500 meters underground

11. Good news again
B. Mottelson noticed that solar neutrinos should have enough energy to form the Ar nucleus in an excited state...
So Bahcall computed the new process, finding that neutrino capture by Cl was increased 20 times

12. Homestake, 1966
The new experiment was built in the Homestake gold mine in Lead, SD
The tank contained 615 tons of C2Cl4 , a normal cleaning agent
By September 1966 it was ready to start making the history of physics

13. How many solar neutrinos?
On the basis of the Standard Solar Model (SSM), Bahcall calculated the solar neutrinos flux on Earth, finding a total of 66 x 109 s-1 cm-2
Unfortunately most of the times the neutrinos have insufficient energy to react with Cl
Moreover nearly all of them would pass through the detector without interaction

14. The SNU
Bahcall expressed the probability that a solar neutrino interacts with a Cl nucleus introducing the Solar Neutrino Unit: SNU=10-36 reactions/nucleus/s
In 400,000 liters of detergent there are about 2 x 1030 Cl nuclei the mean neutrino capture time is 6 days per SNU
Bahcall’s result was SNU and about 6 of these were produced by B8, the ones which Davis’ experiment was able to detect

15. Solar neutrino spectrum
Calculated energy spectrum of the solar neutrinos according to the Standard Solar Model

16. Neutrinos eventually! (but too few)
1968: first results published: the production frequency of neutrinos was too small, 3 SNU at best
In the following years the cosmic-ray background was reduced, the SSM reexamined, while the statistics was slowly accumulating... but neutrinos kept missing
Solar neutrino problem
1978: at the Brookhaven conference it was realized that a new experiment was necessary to detect the neutrinos from the dominant pp fusion
From 1968 to 1988 Davis’ experiment was the only active experiment investigating solar neutrinos

17. Davis’ experiment results*
Davis’ experiment ran continuously until 1994
1998: final results:
2200 Ar atoms produced,1997 extracted
875 counted in the PC: 109 BG events, 776 produced by solar neutrinos
Production rate:
2.56
± 0.16 (stat.)
± 0.16 (syst.) SNU
* The 2002 Nobel Prize in Physics - Advanced Information".
Nobelprize.org. Nobel Media AB Web. 10 Jul 2018.
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18. The ignored solution
In 1968, when Davis’ first results appeared, Pontecorvo and Gribov proposed the right solution to the missing neutrinos
The idea of neutrino oscillations had been first proposed by Pontecorvo (1957) as neutrino-antineutrino transitions
This was later developed to the theory of neutrino flavor oscillation, by Maki, Nakagawa and Sakata (1962) and Pontecorvo (1967)
The theory is based on the existence of two neutrino states
Quantum mechanics allows neutrinos to oscillate between the two states, provided they have mass
The idea that neutrinos have mass, went against the Standard Model of the elementary particles and for this reason the idea was simply ignored

19. Neutrinos from the pp process
Gallium provides the only feasable means to measure the low-energy pp neutrinos
Thanks to a threshold of only MeV for the reaction
with a neutron in the Ga nucleus
The detection frequency of this detector would be 132 SNU, compared to the 7,5 SNU of Davis’ detector

20. All the gallium in the world
Two experiments were built:
GALLEX under the Gran Sasso, Italy
SAGE under the Caucasus mountains, former USSR
Both experiments used the germanium-producing reaction
To build SAGE all the world supply of Ga was necessary
GALLEX had to wait two more years for the production of the Ga itneeded

21. Why two experiments? Both experiments used the same reaction
The composition of the Ga target was metallic gallium for SAGE and a liquid gallium chloride solution for GALLEX
The different forms of the gallium are susceptible to very different types of backgrounds, and thus the two experiments provided a check for each other

22. SAGE (1989-2010) The target was 57 tonnes of liquid Ga metal
Once a month Ge was chemically extracted from the Ga
71Ge undergoes electron capture (T1/2 = days)
The extracted amount of Ge can be determined with a proportional counter by measuring the activity of the resulting Ga atom in an excited state
The excess energy is carried off by low-energy Auger electrons and by X-rays, which, taken together, make for a characteristic decay signature

23. GALLEX* ( )
GALLEX 54-m3 detector tank was filled with 101 tons of a solution of GaCl3 and HCl, for a total of 30.3 tons of Ga
The produced Ge was chemically extracted and detected by counters *

24. Results The SSM predicted 130 SNU
SAGE’s result was 65.4 SNU (based on the data)
GALLEX measured a rate of 77.5 SNU
Both experiments found about half as many neutrinos as expected

25. KamiokaNDE (1983)
The detector was a tank 16.0 m in height and 15.6 m in width, containing 3,048 tonnes of ultra-pure water and about 1,000 PMTs
The aim of the experiment was to find whether the proton decays
Since neutrinos are a major background to the search for proton decay, the study of neutrinos became a major effort
Kamiokande could detect neutrinos in real time, with an obvious advantage on chlorine and gallium detectors
There neutrinos were counted one month after interaction, after radiochemical extraction of the produced Ar or Ge atoms

26. KamiokaNDE II
The detector was upgraded, starting in 1985 to allow it to observe solar neutrinos
As a result the detector KamiokaNDE-II had become sensitive enough to detect neutrinos from SN 1987A
1988: K-II observes solar neutrinos produced by B8
The ability of the experiment to observe the direction of electrons produced in solar neutrino interactions, demonstrated for the first time that the Sun was a source of neutrinos
The number of detected neutrinos resulted too low also for this reaction, about half of what was expected

27. Super-Kamiokande (1996)
Kamiokande failed to detect proton decay, and this led to the construction of Super-Kamiokande
Super-K is a large water Cherenkov detector used to study proton decay and neutrinos from different sources including the Sun, supernovae, the atmosphere and accelerators
The detector is located 1,000 meter underground in the Kamioka mine, Gifu, Japan

28. Super-K detector*
It consists of a cylindrical stainless steel tank that is 41.4 m tall and 39.3 m in diameter holding 50,000 tons of ultra-pure water
The tank volume is divided into an inner detector (ID) region that is 33.8 m in diameter and 36.2 m in height and outer detector (OD, in the remaining tank volume) optically separated from the ID
Mounted on the superstructure are 11,146 PMTs 50 cm in diameter that face the ID and 1,885 20 cm PMTs that face the OD
A cross section of the Super-K detector
* Y. Fukuda et al., Nucl. Instr. and Meth. A 501 (2003) 418

29. Principle of operation
A neutrino interaction with the electrons or nuclei of water can produce a charged particle that moves faster than the speed of light in water
This creates a cone of light known as Cherenkov radiation
The Cherenkov light is projected as a ring on the wall of the detector and recorded by the PMTs
Using the timing and charge information recorded by each PMT, the interaction vertex and particle direction is determined

30. Flavor identification
From the sharpness of the edge of the ring the type of particle can be inferred
The multiply scattered electrons produce fuzzy rings
Highly relativistic muons, in contrast, travel almost straight through the detector and produce rings with sharp edges

31. Solar neutrinos (still missing)
Super-K detected the elastic scattering reaction
which has a relative sensitivity to ne and nm + nt of ~7:1
The 8B solar neutrino flux was calculated to be 2.40 x 106 cm-2 s-1, only of the SSM prediction

32. Atmospheric neutrinos
Atmospheric neutrinos have an energy from tens to several hundred times bigger than solar neutrinos
Neutrino production by cosmic rays
and charge conjugates
is 1 e-neutrino every 2 mu-neutrinos
Since 1985 it was known that the measured ratio of atmospheric muonic to electronic neutrinos was nearer to one than to the expected value of two

33. The anomaly of atmospheric neutrinos
Super-K studied the nm/ne flux ratio by observing final state leptons produced in interactions of neutrinos on nuclei
The flavor of the final state lepton is used to identify the flavor of the incoming neutrino
The quantity
is expected to be 1, if the physics in the Monte Carlo simulation accurately models the data
Super-K was able to determine the incoming direction of neutrinos sufficiently well to tell whether they came from the atmosphere, 10 km above Super-K, or from the other side of the Earth, traveling 13,000 km through the planet

34. Super-K results
1998: the number of upward going (U) atmospheric muon neutrinos (generated on the other side of the Earth) is half the number of downward going (D) muon neutrinos
Studying the asymmetry
no significant asymmetry was observed in the e-like data
the m-like data exhibited a strong asymmetry in zenith angle at high momentum (significantly deviating from expectations)

35. Oscillations, at last
Neutrino oscillations were suggested to explain such deviations
Two-neutrino oscillation hypothesis:
the probability for a neutrino of energy En
produced in a state a
to be observed in a flavor state b
after traveling a distance L is
q and Dm2 are parameters of the hypothesis

36. nm oscillations* Super-K examined two 2-flavor oscillation models: and
The best fit to oscillations was obtained for
The oscillation hypothesis
and the no oscillation hypothesis were both highly disfavored
(*) Y. Fukuda et al., Evidence for Oscillations of Atmospheric Neutrinos, Phys. Rev. Lett. 81,
1562 (1998).

37. nm oscillations
The explanation of the atmospheric neutrino anomaly is:
upward-going muon neutrinos have oscillated into a third neutrino type, the tau neutrino
downward-going muon neutrinos, on the other hand, interacted inside of Super-K before they had traveled far enough to change types

38. 2002 Nobel Prize in Physics
It was awarded to M. Koshiba (Kamiokande) and Davis, but not to Bahcall, “for pioneering contributions to astrophysics, in particular for the detection of cosmic neutrinos”

39. Back to the Solar Neutrino Problem
Was Davis’ problem with electron neutrinos also due to neutrino oscillations?
Pontecorvo and Gribov and Maki, Nakagawa and Sakata explained the solar neutrino problem from the existence of more than one kind of neutrinos
If an electronic neutrino turns muonic in the way between Sun and Earth, it will traverse Davis’ detector without interacting
To verify this idea, a new experiment was built 2100 m underground in a nickel mine in Sudbury, Ontario, Canada: the Sudbury Neutrino Observatory (SNO)

40. The SNO detector n
The detector consists of 1000 tonnes of ultra-pure heavy water enclosed in a 12-m diameter acrylic plastic vessel, surrounded by 7000 tonnes of ultra-pure ordinary water contained in a 34-m high cavity of maximum diameter 22 m
Outside the acrylic vessel is a 17-m diameter geodesic sphere containing 9456 photomultiplier tubes, which detect Cherenkov light emitted as neutrinos are stopped or scattered in the heavy water
The detection rate is of the order of 10
neutrinos per day

41. SNO novelty*
Cl and Ga-based experiments: exclusively sensitive to e-nu’s
H2O-based experiments: predominantly sensitive to e-nu’s
SNO used heavy water (D2O) and measured:
the elastic scattering (ES) reaction nx + e- -> nx + e- active for all neutrino kinds but 6 times more sensitive to ne’s than to other flavors (also used by Kamiokande-II and Super-K)
the charged current (CC) reaction ne+ d -> p +p + e- sensitive exclusively to ne’s (only these nu’s have enough energy to produce the associated lepton)
the neutral current (NC) reaction nx+ d -> p +n + nx equally sensitive to all neutrino flavors
* A. Bellerive et al., SNO Collaboration, Nucl. Phys.B 908 (2016).

42. Neutrino detection
nx + e- -> nx + e- : ES detected by observing the cone of Cherenkov light produced by the electrons
ne+ d -> p +p + e- : CC also detected via the Cherenkov light produced by the electrons
nx+ d -> p +n + nx:
NC initially detected with pure D2O via Cherenkov light from conversion of the 6.25 MeV g ray produced upon neutron capture on deuterium n+ d -> 3H + g
BUT: the neutron capture cross section on deuterium is small + the g ray energy of 6.25 MeV is near SNO’s energy threshold number of NC events was low

43. Neutrino detection nx+ d -> p +n + nx:
NC in a second phase detected with NaCl dissolved in D2O: the thermal neutron capture cross-section for 35Cl is nearly five orders of magnitude larger than that for the deuteron
The Q-value for radiative neutron capture is 8.6 MeV  increase in the released energy led to more observable NC events
the cascade of prompt g rays following neutron capture produced a Cherenkov-light hit pattern very different from that by a single relativistic electron from CC or ES reactions

44. The 8B neutrino flux*
Compared the flux FES(nx) deduced from ES (assuming no neutrino oscillations), to FCC(ne) measured by CC reaction
If neutrinos from the Sun change into other active flavors, FCC(ne) < FES(nx)
SNO found
Reference to Super-K value for FES(nx) was made because of its better precision
The measured value of FCC(ne) is inconsistent with the null hypothesis that all observed solar neutrinos are ne
* Q. R. Ahmad et al., SNO Collaboration, Phys. Rev. Lett. 87: (2001).

45. The 8B neutrino flux Best fit to F(nmt): 3.691.13 x 106 cm-2 s-1
First direct indication of a non-electron flavor component in the solar neutrino flux
Total flux of active 8B neutrinos F(nx): 5.440.99 x 106 cm-2 s-1
In excellent agreement with the predictions of standard solar models
Inferred flux of non-electron neutrinos F(nmt) against the flux of e-neutrinos F(ne)

46. The advantage of being heavy
SNO exploited a reaction unique to heavy water
The use and the advantages of heavy water were proposed by H. H. Chen (1984)
Its use provided a means to measure both electron and non-electron components, and the presence of the latter showed that neutrino flavor conversion was taking place

47. SNO ( )
During 2002 and 2003 the detector was upgraded and any reference to Super-K was no longer necessary
Although Super-K had beaten SNO on time, having published evidence for neutrino oscillation as early as 1998
the Super-K results were not conclusive and did not specifically deal with solar neutrinos
SNO's results were the first to directly demonstrate oscillations in solar neutrinos
The final results were published in 2003:
e-neutrino flux:1.75x106 cm-2 s-1
total flux: 5.21x106 cm-2 s-1, about three times as much

48. Solar Neutrino Problem
conclusions*
Davis had been correctly measuring solar neutrinos for 30 years
For 30 years people had doubted Bahcall, regarding him as ‘the guy who wrongly calculated the flux of neutrinos from the Sun’
His calculation of solar neutrino production was correct; in his words, the agreement was
‘so close that it was embarrasingly close’
* F. Close, Neutrino, Oxford University Press, 2012

49. 2015 Nobel Prize in Physics
It was awarded to T. Kajita (SuperK) and A.B. McDonald (SNO) “for the discovery of neutrino oscillations, which shows that neutrinos have mass”

50. Oscillation parameters
Neutrino mixing is expressed as a unitary transformation U relating the flavor and mass eigenstates
If represents a neutrino with definite flavor (f = e, m, t, …)
and a neutrino with definite mass (i = 1, 2, 3, …)
in the 3-neutrino scenario, the transformation reads

51. PMNS matrix Ufm is the Pontecorvo-Maki-Nakagawa-Sakata matrix
Neglecting a possible Majorana character of neutrinos, U is written
If experiment shows this matrix to be not unitary a new neutrino (sterile neutrino) is required
If d is non-zero neutrino oscillation violates CP symmetry

52. New parameters, new experiments
The existence of oscillations brought into physics 9 new parameters in a stroke:
the three neutrino masses: m1 , m2 , m3
the three mixing angles: q12 , q23 , q13
the CP-violation phase: d
and two Majorana phases
All these parameters are absent from the Standard Model for elementary particles, which, for this reason needs to be reformulated
A host of new experiments was conceived, reactor, accelerator and cosmic neutrino experiments, aimed at studying the new parameters

53. More neutrino experiments
site
additional site
goal
source
begin oper
end oper
CUORE
Gran Sasso, IT -
0nbb
Te130
2016
Borexino
Be7 sun n flux
sun
2007
SOX
n_e,an_e oscillation
Cr51 Ce144
2017
Daya Bay
Daya Bay, PRC
an_e oscillation
6 reactors
KATRIN
Karlsruhe, GE
n_e mass H3
ICARUS
EXO-200
WIPP, Carlsbad, NM
Xe136
2011
LSND
Los Alamos, NM
n_mu oscillation
beam
1993
1998
MAJORANA
Sanford, Lead, SD
Ge76
2015
MicroBooNE
Fermilab, IL
MiniBooNE check
MiniBooNE
n_mu -> n_e
2002
MINERvA
nu scattering
2010
MINOS
Soudan, MN +735
2005
2012
MINOS+
"
2013
NOvA
Ash River, MN +810
n_mu->n_e
2014
DUNE
Sanford, Lead, SD +1300
2022
SciBooNE
MiniBooNE aux
2008
SBND
SNO
Sudbury, CA
n_e oscillation
1999
2006
SNO+
Kamiokande II
Kamioka, JP
sun, atmosphere
1985
1995
Super-K
1996
K2K
Tsukuba, JP
Kamioka, JP +250
n_mu -> n_tau
2004
T2K
Tokai-280m, JP
Kamioka, JP +295
IceCube
South Pole
cosmos
Antares
Toulon, FR
n flux
Chooz
Chooz, FR
2 reactors
Double Chooz

54. References
Most of the material in the presentation was found in the beautiful book ‘Neutrino’ by Frank Close, Oxford University Press
Physicist portraits were downloded from the web
Much useful information was found on Wikipedia pages – support Wikipedia!